| paper | d4-conf-aaai-2010-0032 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
Theorem 16 and Proposition 17 bound properties of choice rules; neither makes a claim about computing a result or the complexity of finding a rule. The unnumbered LP is used for small-\(n\) experiments, but supplies no named computational result, so bit (a) fails.
fails bit a — no named computational result to mirror
The proposed participant-mass extension concerns Theorem 16 and Proposition 17, but neither survives as a computational mirror; the paper's other results are not covered.
The strongest honest positive lead is a continuum of tournament participants, but this paper gives no qualifying named computational result to anchor it.
The closest result is Theorem 16, proved in the paper: for tournaments on \(n\) alternatives, no choice rule that is 3-SNM can have Condorcet consistency value \(\alpha>2/n\). Proposition 17, also proved here, says that no 2-SNM choice rule can have \(\alpha>2/3\). These are bounds on the existence of rules, not results about computational complexity. The paper’s LP for maximizing the 2-SNM guarantee is described in the text and used to compute small cases, but it is not presented as a numbered result.
A possible adjacent question would model a large tournament as a distribution over participant types, with mass representing the share of participants of each type; a rule would assign winning probability across those types, and a coalition’s action would change pairwise outcomes within the coalition. One could ask whether Theorem 16’s \(2/n\) bound has a meaningful limit in that model. But this is an axiomatic extension, and defining types and lotteries so they preserve the paper’s individual-level manipulation is a substantial obstacle. It is not a computational mirror of a named result.
So I cannot give the requested prover-ready continuous problem per anchor without misrepresenting the paper. The paper studies manipulation and randomized choice rules, but its named results concern axiomatic existence and bounds, not algorithmic complexity.
The proponent’s strongest point also defeats their proposed anchor: the paper has no named computational result to continuize. Theorem 16 and Proposition 17 are bounds on the existence of tournament choice rules. Proposition 12 gives axiomatic properties. The LP for maximizing the \(2\)-SNM guarantee is a finite optimization formulation, used for small-\(n\) experiments, but the paper proves no complexity result about it. So none supplies the computational question ChoCo asks analysts to mirror.
The natural voter-population model does not repair that gap. A distribution over rankings induces a pairwise tournament, but the paper’s manipulators are the alternatives themselves. It studies coalitions that flip edges among their members, not voter coalitions changing the society. And the rule sees only each edge’s direction: different voter distributions with the same majority relation give the same input. Continuizing voters therefore adds no population variable to the paper’s manipulation problem.
The stronger alternative is to treat the tournament participants as a population of types. But the paper’s results concern coalitions of a fixed number of participants and the winning probability of particular alternatives. In an atomless population, a fixed-size coalition has zero mass, and an individual alternative has zero probability under a lottery represented by a measure. Recasting the question around positive-mass coalitions and type-level winning probability could be a sensible new axiomatic problem; it would not preserve the theorem’s target, and it still would not create a computational result to mirror.
One could study the complexity of the paper’s LP as \(n\) grows. That may be worthwhile on its own, but its variables range over tournament structures and alternatives, not population multiplicities. The paper gives no reason to expect a high-multiplicity regime to compress that structure.
I cannot prove that no one could devise a recognizable mass-based reformulation. The honest negative case is narrower: every plausible route changes the object being studied or lacks a computational result to anchor a mirror. The proponent’s tentative questions about Theorem 16 and Proposition 17 do not survive the programme’s gate.
The adversarial triple: the proponent anchors on up to three named results; the opponent sees that case and must defeat every anchor; the judge decides which case convinced it. These are the pipeline’s own outputs, generated by tools/triple_run.py — no human edited them. The paper’s own text is not reproduced here beyond the quoted statement above.